function y = kernel_m_singular_nonmod_2_analytical(zeta, m, CONSTS)

    k0 = CONSTS.k0;
    a = CONSTS.a;
    c = CONSTS.c;
    eps_a = CONSTS.eps_a;
    eps = CONSTS.eps;
    eta = CONSTS.eta;
    
    Z0 = 4*pi/c;
    
    y = 1i*Z0*(k0/(2*pi))*(-(2*m^2*eps_a)/(((k0*a)^2)*(eps_a^2+abs(eps*eta)))) * ...
        (log(abs(zeta)./(2*a)) + log(sqrt(eps/abs(eta))) + 4*((sum(1./(2*(1:(abs(m)))-1))) - log(2)));

end